To balance the chemical equation for the combustion of ethane (C₂H₆), we follow these steps:
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Write the unbalanced equation: \[ \text{C}_2\text{H}_6 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]
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Count the number of atoms of each element on both sides.
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Start by balancing the carbon (C) atoms:
- There are 2 carbon atoms in C₂H₆, so we need 2 CO₂: \[ \text{C}_2\text{H}_6 + \text{O}_2 \rightarrow 2 \text{CO}_2 + \text{H}_2\text{O} \]
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Next, balance the hydrogen (H) atoms:
- There are 6 hydrogen atoms in C₂H₆, so we need 3 H₂O to get 6 hydrogen atoms: \[ \text{C}_2\text{H}_6 + \text{O}_2 \rightarrow 2 \text{CO}_2 + 3 \text{H}_2\text{O} \]
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Now, count the oxygen (O) atoms on the right side:
- From 2 CO₂, there are \(2 \times 2 = 4\) oxygen atoms.
- From 3 H₂O, there are \(3 \times 1 = 3\) oxygen atoms.
- Total: \(4 + 3 = 7\) oxygen atoms.
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Now, balance the oxygen (O) on the left side:
- The O₂ molecule contributes 2 oxygen atoms, so we need \(\frac{7}{2}\) O₂ molecules to get 7 oxygen atoms. To eliminate the fraction, multiply the entire equation by 2: \[ 2 \text{C}_2\text{H}_6 + 7 \text{O}_2 \rightarrow 4 \text{CO}_2 + 6 \text{H}_2\text{O} \]
Now the balanced equation is: \[ \boxed{2 \text{C}_2\text{H}_6 + 7 \text{O}_2 \rightarrow 4 \text{CO}_2 + 6 \text{H}_2\text{O}} \]